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We prove the inequality λ 2 [V 1 ]−λ 1 [V 1 ]≥λ 2 [V 0 ]−λ 1 [V 0 ] for the difference of the first two eigenvalues of one-dimensional Schrodinger operators −d 2 /dx 2 +V i (x), i=0,1, where V 1 and V 0 are symmetric potentials on (a,b) and on (a,(a+b)/2), and V 0 −V 1 is decreasing on (a,(3a+b)/4)

The gap between the first two eigenvalues of a one-dimensional Schrödinger operator with symmetric potential